Tax Evasion and Productivity
Hans Martinez
Western University
April 19, 2023
Outline
- Does the empirical results and identification depend on the linearity of the PF?
- Who are the compliers, the small firms or the big firms?
- Size defined by what measure?
Preview
- Tax evasion estimates using a CD PF might be a lower bound if the derivative of the true PF is monotonic in \(m^*\)
- Even though very big firms do not overreport inputs, they might be very few to statistically learn from them
- Alternatively, using small firms might provide lower bound of tax evasion because they do not evade as much as large firms
Departing from CD
\[
\begin{aligned}
\mathbb{E}\left[\ln\left(\frac{\rho M^*}{PY}\right)\right] &= \mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*+\varepsilon_{it}^M)\right)\right]+\ln\mathcal{E}+\mathbb{E}[\varepsilon_{it}^M] \\
&= \mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*)\right)\right]+\delta+\ln\mathcal{E}+\mathbb{E}[\varepsilon_{it}^M]
\end{aligned}
\]
where, \(\delta\equiv\mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*+\varepsilon_{it}^M)\right)\right]-\mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*)\right)\right]\)
Departing from CD
\(\frac{\partial }{\partial m^*}f(\cdot)\) can still be recovered from compliers
\(\delta\ge0\) if \(\frac{\partial }{\partial m^*}f(k_{it},l_{it},m_{it}^*+\varepsilon_{it}^M)\) is monotonic in \(m_{it}^*+\varepsilon_{it}^M\)
\(\delta\) is a function of \(\varepsilon^M_{it}\) and therefore not independent from \(\mathbb{E}\left[\ln\left(\frac{\partial }{\partial m^*}f(\cdot)\right)\right]\)
CD as a lower bound
CD PF ignores the non-linear effect \(\delta\), however it can be considered a lower bound
The tax evasion may be greater than what CD suggests because \(\delta\ge0\)
Alternatively, because \(m^*_{it}\) is not observed separately from \(\varepsilon_{it}^M\), using a PF with a derivative that is monotonic in \(m_{it}^*+\varepsilon_{it}^M\) might affect estimates of tax evasion
Translog PF
In the case of the translog PF when there is only \(K\) and \(M\)
\[
\begin{aligned}
\mathbb{E}\left[\ln\left(\frac{\rho M^*}{PY}\right)\right]=\mathbb{E}&\left[\ln\left(\beta_0 +\beta_K\ln K+\beta_M \ln M^*+\beta_M\varepsilon_{it}^M\right)\right]\\
&+\ln\mathcal{E}+\mathbb{E}[\varepsilon_{it}^M]
\end{aligned}
\]
How to estimate?
Hu et al. (J. Econom. 2022)
\[
\begin{aligned}
Y &= m_0(X^*) + \eta\\
X &= X^* + \varepsilon
\end{aligned}
\]
- Zero conditional mean \(\mathbb{E}[\eta|X^*]=0\)
- Independence \(f_{Y|X^*,X}(y|x^*,x)=f_{Y|X^*}(y|x^*)\)
- Normalization \(G[f_{X|X^*}(\cdot|x^*)]=x^*\)
- Monotonicity \(m_0\) is strictly monotonic in \(X^*\)
- Then, \(m_0\) is identified even when \(X^*\) and \(\varepsilon\) are correlated
Who are the compliers?
- Very big firms do not evade taxes by overreporting inputs; more sophisticated,
- e.g., profit shifting, they can afford long legal disputes with authority to avoid paying taxes
- Ecuadorian evidence: The probability of having ownership of a ghost client increases with individuals’ income
- Stronger incentives to avoid illegal behavior
Who are the compliers?
- Large firms evade more through overreporting
- Ghost clients have higher revenues, costs, and tax liabilities.
- The probability of engaging in cost overreporting increases monotonically in firm revenue Higher volume of transactions. Fake invoicing limits to cash transactions. Cash transactions are capped in Ecuador.
- Share of ghost deductions also increases throughout much of the size distribution, except at the very top
Who are the compliers?
- Small firms evade by overreporting but by a small amount
- Small firms are less sophisticated (owner’s income)
- Small firms have a lower volume of transactions, so higher probability of getting caught if they cheat, so they cheat but a little
Who are the compliers?
It is still likely that very large firms do not overreport costs but they might be very few to statistically learn from them
Alternatively, using small firms to learn about tax evasion can provide a lower bound of tax evasion
Empirical evidence
Empirical model
\[
\begin{aligned}
s_{it}&=\beta_0+\beta_1D(Compliers)+\gamma_J+\varepsilon_{it}^Y\\
s_{it}&=\beta_0+\Phi(k,l,m)+\beta_1D(Compliers)+\gamma_J+\varepsilon_{it}^Y
\end{aligned}
\qquad(1)\]
- \(D(Compliers)\): dummy variable, 1 if the firm is a complier; 0, otherwise
- \(\gamma_J\): industry fixed effects
- \(\Phi(\cdot)\): second degree polynomial
Empirical evidence
Graphs report percentage deviations of compliers from the rest of the firms, controlling for industry
\(\Delta\%=exp(\beta_1)-1\). Why?
\[
\begin{aligned}
\ln\beta_{Compliers}&=\hat{\beta}_0+\hat{\beta}_1\\
&=\ln\beta_{Evaders}+\ln\Delta\\
&=\ln(\beta_{Evaders}\times\Delta)\\
\implies \Delta &=\frac{\beta_{Compliers}}{\beta_{Evaders}}\\
\implies exp(\hat{\beta_1})-1&=\frac{\beta_{Compliers}}{\beta_{Evaders}}-1\\
&\equiv \Delta \%
\end{aligned}
\]
Summary
- CD functional form suggests Tax Evasion lower bound
- If very large firms are too few, I might use small firms knowing they cheat a little
- Maybe I won’t be able to pick a measure of size until I get access to validation data
Next steps
- Compliers: explore exporters (sophisticated), ISO certified firms (third-party reporting)
- Repeat exercise with Ecuadorian data
- Move forward to deconvolution for CD and Hu et al.(2023) for NLPF
Outline
- Looking ahead
- The Job Market
- Miscellaneous
- JMP update
- Ecuadorian data
- Measure of size: 1) Data; 2) Carrillo et al.
- Next steps
Looking ahead
- Plan: 2024 JM
- Have JMP mostly done by the 2023 Fall
- Apply to conferences by Early 2024 Winter
- Present at conferences during 2024 Summer
- Go to Job Market Fall 2024
Miscellaneous
- Funding, out by 2023 summer; ~$3K monthly (tuition, rent, services)
- Teaching
- Graduate Fellow rather than Graduate Student Assistant
- 2nd and 3rd papers
- Are you OK working with multiple projects simultaneously?
- Summer Paper with new twist and 2) new idea
Misc 2
- Networking
- Cold email: Targeting canadian universities with a PhD program located in cities with manufacturing sector
- CEA
- Applying for PR (Canadian market)
- Goal to submit docs by end of 2023 summer
- Took English Test (CELPIP-G) (March 18, 2023)
- Next: ECA’s
- Web page (done!), research (draft) and teaching (to do) statement
Upcoming presentations
- UWO Applied Seminar: May 24, 2023
- CEA, Winnipeg, Manitoba: June 2-3, 2023
JMP update
- Ecuadorian Tax data:
- Agustin Carvajal, a former member of Ecuador’s Fiscal Research Institute (now extinct), is willing to provide access to data
- Data can only be accessed in Ecuador
- Paul Carrillo, author of Tax Evasion paper, agreed to talk
- Ecuadorian firm data:
- Now using Manufacturing and Mining Survey (EMM), which includes small, medium, and large firms before, Structural Survey only covers large firms
- Still fewer observations than Colombian data (Colombia’s manufacturing GDP is 2.5+ times bigger than Ecuador’s)
Measure of firm size
Who are the non-evaders? What’s the threshold of size?
- Data:
- Last time: \(exp\left(E\left[\ln\left(\frac{\rho M}{PY}\right)\Big | S\ge s\right]\right)=\beta\)
- Today: adding confidence intervals, keeping labor and capital, adding alternative measures of size lag of paid taxes, sales, and production
- Ecuador paper: eye-balling ~95-98 percentile of firm revenue
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Carrillo et al., 2022
Summary
- Using Labor (number of employees, and number of employees \(x\) years, and somewhat less total wages) as measure of firm size is consisten with my model
- Different bias magnitude for different industries suggest different opportunities for tax evasion through cost overreporting — which makes sense!
- High \(\beta\)’s for top deciles of lag taxes, lag output, and lag sales suggest there might be a dynamic component in tax evasion
- Firms might adjust their prior probabilities the next period. If they were not caught cheating, they might cheat again
Next steps
- Repeat the exercise with Ecuadorian data
- Select industries in both countries
- Deconvolution using Labor as the measure of firm size
- Model?
- Structural model counterfactual estimation for showcasing in JM
Job interests
- What?
- Academia
- Research-focused non-academic: government agency, tech company, consulting
- Where?
- Canada
- Mexico
- USA